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GMAT Algebra Questions
Practise algebra (mathematics) for the GMAT Focus Edition: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Algebra practice
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Q1.Solve: x² − 14x + 45 = 0
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Answer: B — 5, 9
Find two roots with sum 14 and product 45: 9 and 5. So x² − 14x + 45 = (x − 9)(x − 5) = 0.
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Q2.Find the sum of the first 8 terms of the AP 5, 7, 9, …
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Answer: B — 96
Sₙ = n/2 × [2a + (n − 1)d] = 8/2 × [10 + 14] = 96.
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Q3.Solve: 4x + y = 42 and x + 4y = 3
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Answer: C — x = 11, y = -2
Elimination/substitution gives x = 11, y = -2. Check: 4(11) + 1(-2) = 42 ✓ and 1(11) + 4(-2) = 3 ✓.
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Q4.Solve: x² − 8x + 15 = 0
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Answer: B — 3, 5
Find two roots with sum 8 and product 15: 5 and 3. So x² − 8x + 15 = (x − 5)(x − 3) = 0.
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Q5.Solve: x + 5y = 16 and x + 3y = 14
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Answer: A — x = 11, y = 1
Elimination/substitution gives x = 11, y = 1. Check: 1(11) + 5(1) = 16 ✓ and 1(11) + 3(1) = 14 ✓.
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Q6.Find the sum of the first 23 terms of the AP 10, 18, 26, …
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Answer: D — 2254
Sₙ = n/2 × [2a + (n − 1)d] = 23/2 × [20 + 176] = 2,254.
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Q7.Find log₅ 25.
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Answer: B — 2
log_5(25) asks “5 to what power gives 25?” → 5^2 = 25, so the answer is 2.
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Q8.Find log₃ 243.
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Answer: A — 5
log_3(243) asks “3 to what power gives 243?” → 3^5 = 243, so the answer is 5.
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Q9.Solve: 2x + 3y = 27 and 5x + 5y = 65
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Answer: B — x = 12, y = 1
Elimination/substitution gives x = 12, y = 1. Check: 2(12) + 3(1) = 27 ✓ and 5(12) + 5(1) = 65 ✓.
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Q10.Find log₂ 8.
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Answer: B — 3
log_2(8) asks “2 to what power gives 8?” → 2^3 = 8, so the answer is 3.
How to approach algebra questions
Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution. For simultaneous equations, elimination is usually faster than substitution under time pressure.
About GMAT
GMAT Focus Edition — conducted by Graduate Management Admission Council (GMAC). Business-school admission test with Quantitative Reasoning, Verbal Reasoning and Data Insights.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
GMAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Ratio, Ages & Mixtures | Quantitative aptitude | Calculated (new numbers every set) |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Data Interpretation | Data interpretation | Calculated (new numbers every set) |
| Verbal Reasoning & Analogies | Reasoning | Calculated + question bank |